There will be no significant difference between sodium associated with Iodide and potassium associated. The average intake of potassium in the USA is about 2000 milligrams. They should be averaging about 3500 milligrams if they ate no junk food (see http://charles_w.tripod.com/arthritis3.html.
Sodium is in a similar kind of amount bracket. Since almost no one is getting more than 20 milligrams of potassium or so from Iodide supplements, the amount of potassium additional from Iodide supplements would be insignificant. So would the sodium status be insignificant.